Integrability of Van der Pol–Duffing oscillator system in three‐dimensional vector field

摘要

In this work, we focus on studying the integrability of the following three‐dimensional Van der Pol–Duffing system x˙=−m(x3−μx−y),y˙=x−y−z,z˙=βy. More precisely, if m β ≠ 0, then the above system has no analytic and nor Darboux first integrals at the neighborhood of the origin. Also, the stability and instability of the singular points are employed to investigate the C1 integrability of this type of system.